About Me

I'm a Visiting Professor of Philosophy at the University of Ulsan in South Korea. I successfully defended my PhD dissertation ("Truth is a One-Player Game: A Defense of Monaletheism and Classical Logic") last March. I also have an MFA in Creative Writing from the Stonecoast program in Maine. Oh, and I go out at night to fight crime, under the alias "the Caped Logician."
Actually, that last sentence was a lie. (As is this one.) But, according to some people, I am an enemy of "Christendom."

Wednesday, March 30, 2011

Imagine a world where the predicates 'is green' and 'is colored' were considered much more philosophically interesting than it is in the actual world, interesting enough that philosophers and logicians worried about what formal rules related these predicates. One fairly crushingly obvious rule about them would what we can call the G-out rule, allowing us to infer 'X is Colored' from any instance of 'X is Green.'

Now, imagine that there was one other big difference between that world and this world. In our world, the classical example of a syntactically correct but clearly meaningless sentence is C:

C: "Colorless green ideas sleep furiously."

In the imaginary world, this sentence is treated rather different. The humans in this world have made contact with unfathomably intelligent alien entity, capable of speaking English (perhaps with the aid of a universal translator). Every time the entity has been asked a question, and it has deigned to answer, its answer has been proven correct. Sometimes it has taken humans many years, and full-fledged scientific revolutions, to understand *how* what the entity said could have been true, but in the end, there's never been any room for serious doubt. The entity has never once been shown to have (or even been widely suspsect to have) misunderstood a question. At some point, for some strange reason, someone asks the entity about C and it points to the paper where the questioner has written down C and says "this is true."

As often happens when the alien entity says something interesting, ripples of immediate change go through entire fields of study. A few philosophers think that in this case the entity got confused and make a strange sort of category mistake--after all, as in our world, any position, no matter how odd, always has a few philosophical backers--but there's a wide consensus now that C must be true (and therefore meaningful) after all. Almost immediately, some clever theorists notice that this revelation has created a new problem, which they call the "Greenness Paradox." Pretty soon, the dialetheists in this world seize on the Greenness Paradox as an argument for the existence of true contradictions. Here's how it goes:

Start with the formalization of C, given classical logic and orthodox assumptions about how to read the existential quantifier:

1: "There exists an X such that X is green and it is not the case that X is colored and X is an idea and X sleeps furiously."

It clearly follows from 1 that:

2: "There exists an X such that X is green and it is not the case that X is colored."

Apply existential instantiation to 2 to get:

3: "P is green and it is not the case that P is colored."

Apply conjunction elimination to 3 to get:

4: "P is green."

Apply our G-out rule to 4 to get:

5: "P is colored."

Apply conjunction elimination to 3 once again to get:

6: "It is not the case that P is colored."

Apply conjunction addition to 5 & 6 and we get:

7: "P is colored and it is not the case that P is colored."

.....which, the dialetheists of this world argue, is a true contradiction! Viola.

Of course, the dialetheist take on the Greenness Paradox isn't the only game in town. For example, one would imagine that a more conservative solution to the Greenness Paradox would be to deny "the naive theory of greenness" and to restrict G-out in some way. An obvious non-classical but non-dialetheist solution would be to deny that the existential quantifier is ontologically loaded after all. Proponents of this Meinongian solution to the Greenness Paradox would argue that some things can be true of colorless green things ideas without there being colorless green ideas. The Hofweber of this world will argue that, while the existential quantifier is ontologically loaded, and classical logic and the naive theory of greenness are true, and we shouldn't be so arrogant as to reject the superior wisdom of the alien entity by denying C, truth preservation should be understood in a generic rather than universal way. Just as "bears are dangerous" can be true without every bear being dangerous, "valid logical inferences are truth preserving" can be true even if not every valid inference from a true premise preserves truth. The Greenness Paradox, Bizarro-Hofweber would argue, shows us that the universal reading of the notion of truth preservation represents an airy "ideal of validity" that has an obvious appeal, but that the paradox falsifies the ideal.

At this point, it should be pretty easy to come up with a variety of other such philosophically sophisticated solutions to the paradox and to have a pretty good idea of how the argument between proponents of various competing solutions would proceed. Inevitably, some solutions would seem to work better than others, to contain hidden inconsistencies, and so on, and everyone, including the few extreme skeptics who didn't think the unfathomably intelligent alien entity at the source of all this was on the level when it uttered the words "this is true" about C, would be able to do so perfectly easily. "You try to solve it by saying that the colorless, furiously sleeping ideas are red rather than green, but red things are just as colored as green ideas, so you haven't gotten around the original problem." "You forgot a negation sign in Step 5. Once you add it in, you can see that a contradiction is entailed later, when you say...." Etc., etc., etc.

Now, imagine that they were right, and that the entity actually had the same take on C as Chomsky and most of the rest of us citizens of the actual world. He was simply messing with the puny humans out of boredom by pointing to a meaningless sentence and saying the words "this is true." He'd never done this before--he'd always given good and helpful responses to the rest of their inane little queries--but there's a first time for everything. Certainly, from the perspective of the humans, it's understandable that they would never catch on. Having been shown so many amazing things by the entity--remember, scientific revolutions are sparked off by it's statements on a regular basis--it seems utterly plausible to them that a sentence they thought was definitely meaningless actually has a meaning that their puny monkey minds cannot fully grasp. From there, given the function of phrases like 'is green' and 'is colored' in meaningful sentences (G-out is clearly a good rule), the equivalence of 'colorless' with the negation of 'colored', and the ways that we translate into logical lingo sentences of the form "X-ish things do Y", the apparent possibility of reasoning from a contradiction to Y.

Now, assuming that we and the imaginary aliens are right about C, we now have a problem. It is, in fact, the same problem we ended Part I with. We know that nothing "follows" from C. It's meaningless, not the kind of thing we can logically symbolize or apply truth-talk to without committing a nonsensical category mistake. The idea that anything really "follows" from C is deeply confused, like saying that something 'follows' from a string of nonsense syllables, or a bit of burning candle wax. Somehow, though, we seem to be perfectly capable of 'reasoning' about it, as we've been doing for the last few paragraphs.

In the beginning of Part I, I argued that the diquotationalist "nothing above and beyond" principle about truth--"to say that 'P' is true is to say nothing above and beyond P", or to put it differently, "to prefix a quoted sentence with the words 'it is true that' has the semantic effect of simply removing the quotation marks" (the claim, remember, from which the word "disquotationalism" is derived)-is best explained by a general view that the truth predicate/operator is only parasitically meaningful. Of course, the original claim is about sentences that ascribe truth to sentences quoted within them and my claim broadens this to all ascriptions of truth, but I would argue that the former claim, in the absence of the latter, has some awkward consequences. For example, consider the following three sentences*:

I'd submit that there's something a bit strange about arguing that (11) and (12) have distinct meanings. If one asserts meaning-parasiticalness for sentences that ascribe truth to an internally quoted sentence and rejects meaning-parasiticalness for sentences that ascribe truth to other sentences in other ways, one has to explain what substantive difference the *method* of applying the predicate/operator to the claim to which truth is being ascribed makes. Moreover, the obvious explanations of *why* the "nothing above and beyond" principle would be true--most obviously, general philosophical stories like "the word 'true' doesn't pick out some substantive feature of the world, but rather functions as a time-saving way of saying other things, especially useful for cases where we aren't entirely sure *what* we're saying (i.e. blind endorsements)"--would seem to apply equally well, to sentences like (11), sentences like (12), to sentences like "everything John just said is true", to the one-word exclamation "true!" uttered in response to something one's friend has just said, and so on. The syntactic form the truth-ascription takes seems to make no difference. All sentences that do nothing but ascribe truth to a sentence inherit their meanings from the meanings of the sentences to which they ascribe truth. If a sentence S1 tries to ascribe truth to another sentence S2 that has no meaning, S1 will have no meaning either. It has nowhere to get it.

A happy consequence of this view is that, given some other plausible assumptions (e.g. that adding the word "not" to a meaningless sentence does not convert it into a meaningful one), it entails that sentences like "this sentence is not true" are meaningless. This lets us solve the Liar Paradox without having to give up on "the naive theory of truth"--a unitary truth predicate obeying all the standard rules about truth, etc.--or the unrestricted power of classical logic, or much of anything else except many people's initial intuition that the sentences involved are meaningless. At the end of Part I, though, we confronted what sounds like a serious problem:

Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)

(8) The sentence marked as (8) does not express a true proposition.

If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.

Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):

(9) The sentence marked as (9) has some status other than 'true.'

....or the familiar anti-dialetheist revenge paradox (10):

(10) This sentence is just false, rather than being both true and false.

.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?

Now, there's a lot more to be said about all this--particularly about the thorny question of what sort of mistake someone can be accused of when they 'reason' about something meaningless in a 'bad' way and 'contradict' themselves about it, above and beyond the original sin of treating the something in question as if it were meaningful--but I take the example at the beginning of this post to pretty definitively answer the question I ended the last post with in the negative. Someone who (as we would all agree here in the actual world, correctly) characterized C as meaningless would be faced with precisely the same problem that a pardadox-solver who takes the Liar to be meaningless is faced with in our world. Although it's still somewhat unclear *why* the objection doesn't work in either case--we'll say more about that--it's failure in the closely parallel imaginary Greenness Paradox case would seem to show that it fails when it comes to the actual Liar Paradox as well.

Monday, March 28, 2011

I'm once again putting off Part II. I've written about half of it, but (i) I have tests to write and classes to prep, and (ii) I just finished writing what, on copying and pasting all of my comments into a Word file and running a word count, turned out to be a bit over 2500 words in response to Colin, Brandon and ParisW's thoughts and objections to Part I. If you're desperate for more material on Liars and meaninglessness, I'll direct you to that discussion-in-progress. Meanwhile, I'll mention that this last weekend I was interviewed for a second appearance on the philosophy-themed Diet Soap podcast. Sounds like I might Episode 100. We didn't really skip to this script (plenty of questions not on the list, not all of the list questions asked), and in any case the interview lasted long enough that only a fraction of it should survive the cutting process and make it into the podcast, but to give at least an approximate flavor of the interview, here are the questions that host Doug Lain sent me in advance...

#

You have a doctorate in philosophy and you specialize in philosophical systems of logic. As an American philosopher and a logician it strikes me that you'd fall in with Analytic philosophers. Is this correct?

How do you consider the division or distinction between continental and analytic philosophy?

How important is Frege, Russell and Wittgenstein to you and your philosophical work.

Do you hold to a deflationary account of truth claims?

It seems to me that Analytic philosophy might share something in common with instrumental reason. That is, that the deflationary accounts of truth claims have the impact of limiting our ability to challenge the logic of our historical moment or culture, whereas Continental philosophers like Hegel and Neitzche were primarily interested in thinking about how philosophy was tied to culture and history.

Wednesday, March 23, 2011

No time for a second post in the series on the meaninglessness solution to the Liar Paradox just now--my apologies, dear reader, but you'll have to wait until Monday for that--but, to reward you for checking back for one, here's a link to a comic that the sort of people who read this blog might enjoy.

(And, on the other end of P.F. Snow's 'Two Cultures', this one's good too.)

...and, for precisely, the same reason, "Truth-Teller" sentences, like:

(3) The sentences marked (3) is true.

....and, of course, conditionalized truth-tellers (better known as "Curry sentences"), like

(4) If this sentence is true, the author of the blog post it appears in is a dialetheist.

.....are quite literally meaningless. "Wait," I can hear you asking, "doesn't that make (2) true?" I've written extensively about that question in the past, but the short answer is "no." A sentence with the grammatical form of a disjunction and a "second disjunct" that, if the same words in the same order were split off into a sentence of their own, would constitute a meaningful-and-true sentence, does not thereby become a meaningful sentence, much less a true one. For example, take (5), adapted from the classical example of a meaningless-but-"well-formed" sentence:

(5) Either colorless green ideas sleep furiously or snow is white.

There is, clearly, no contradiction in asserting both (6):

(6) (5) is meaningless.

....and (7):

(7) Snow is white.

....at the same time. Now, this is a very unpopular solution to the paradoxes--which is part of what makes it interesting enough to spend years developing arguments for!--but one which there are few extensive arguments against. Many theorists interested in the paradoxes--especially those interested in non-classical approaches--just brush it off out of hand as not worth taking seriously. Graham Priest derisively refers to it in In Contradiction as "the heroic solution." Hartry Field says in the introduction to Saving Truth From Paradox that people who endorse meaninglessness solutions must mean the term "meaningless" in "some special technical way", so that what they're saying must amount to a strangely-expressed version of his own paracomplete solution.

(I've always tried to be clear that I mean the word "meaningless" is precisely the ordinary mundane sense. As a result of my version of extreme deflationism about truth, I take the sentences that JC Beall calls "TTruth-inelimable" to be literally meaningless in precisely the same sense as a string of nonsense syllables, or "Colorless green ideas sleep furiously." Click on the link above for a less abbreviated explanation, but, basically, I agree with and take literally Quine's claim that sentences that ascribe truth to other sentences mean nothing above and beyond what the original sentences mean--that's the original metaphor behind the term "disquotationalism," that the upshot of prefixing a quoted sentence with the words 'it is true that' is to "remove the quotation marks"--and I generalize this to the claim that all truth-ascribing sentences necessarily inherit their meaning from the sentences to which they ascribe it. Thus, for example, "'colorless green ideas sleep furiously' is true" ends up being meaningless, because it inherits no meaning from the sentence to which it tries to ascribe truth. For precisely the same reason, "this sentence is true" is meaningless. And, of course, as Carnap was fond of pointing out, the negation of nonsense is nonsense.)

In the same spirit as Field's disguised-paracompleteness objection, when I met a regular reader of this blog, at the Eastern APA before last, we chatted about the Liar Paradox and he said he'd have to wait to "see the technical details" before he knew if it would "work."

I have, of course, a philosophical argument for the claim, and a lot of responses to various actual and potential objections, by the very nature of the solution, there aren't and can't be any "technical details." (There's plenty of nit-picky precision work--particularly when it comes to formulating and responding to "revenge paradoxes"--but that's not what most Liar specialist mean when they talk about "technical details.") The necessary absence of technical details strike right at the heart of the difference between the meaninglessness solution and more standard ones--that nothing technical needs to be revised in any way, shape or form on account of the semantic pardoxes is one of the chief selling points of the solution! We get to keep "the naive theory of truth" rather than any of the elaborate 'technical' theories that have proliferated in the post-Tarski/post-Kripke era. We get to keep classical logic, classical T-in and T-out rules, and, in short, we get to keep everything except for the intuition that many professional philosophers report having about the semantic status of the sentences in question.

So no, no "technical details" of the kind fashionable in theories of the Liar. There are not and could not be special rules (whether thought of as logicially revisionary or placed 'on top of' the logical edifice regulating particular predicates or operators related to truth or meaninglessness) about, say, the precise behavior of M(P) and ~M(P), because, if a sentence is meaningless, to symbolize it with a letter and trying to perform logical operations on it is to commit the same nonsensical category mistake which would be committed if some very confused logician tried to do the same to a cough or a string of nonsense syllables or a bit of burning candle wax.

The most common argument against the meaninglessness sentence is a simple foot-stamping appeal to intuition. Sadly, X-phi has not yet provided us with any empirical evidence about how widely shared the intuitions in question are, so it's hard to know whether those who take it as obvious that such sentences are meaningful are right when they assert that it's generally obvious to everyone pre-philosophically, but whether they're right or wrong, it's clearly possible for competent speakers of a natural language to be mistaken about questions of meaningfulness. For example, the philosophers of the Vienna Circle were competent speakers of German, but they mistakenly took many perfectly meaningful German sentences about metaphysical subjects to be meaningless. In fact, even if we *wanted* to be semantic Cartesians, holding idealized views about the privileged access of competent speakers to the status of sentences as meaningful or meaningless, we couldn't, because there are disputes in which, whoever is right, someone is a competent speaker making this mistake. For example, Graham Priest and I are both competent speakers of English, and we disagree about the meaningfulness of Liar sentences. Whichever one of us is right, the other one is a competent speaker of a natural language who has made a mistake about meaningfulness.

Of course, there's nothing wrong with appeals to intuition--we can hardly do without them entirely--but, given a good argument and a good error theory, initial intuitive assessments are often shown to be false. Arrogantly enough, of course, I take myself to have both.

What about, however, the following more sophisticated variant on this sort of objection? (It was presented to me by a junior faculty member at the University of Miami a year or so ago, and I don't think I took it seriously enough at the time.) Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)

(8) The sentence marked as (8) does not express a true proposition.

If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.

Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):

(9) The sentence marked as (9) has some status other than 'true.'

....or the familiar anti-dialetheist revenge paradox (10):

(10) This sentence is just false, rather than being both true and false.

.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?

Wednesday, March 16, 2011

One of the classes I'm teaching this year is, basically, a political philosophy class for Sociology majors. Following the Sociology Department's recommendation, I'm assigning Michael Sandel's book "Justice: What's The Right Thing To Do?"

It has some important secondary advantages--e.g. it's available in Korean translation--and, to be fair, it's reasonably well-written. Sandel uses lots of nice, vivid historical examples. But in some ways.....Jesus.

To steal a line from Jay Rosenberg, Sandel's critique of utilitarianism commits genocide against an entire race of straw men.

Monday, March 7, 2011

Wednesday, March 2, 2011

I talked about Part I on Monday. Part II just went up. My questions were the last four included. I also contributed the clarification to the next-to-last question, obviously.

There's a lot of interesting stuff here, a good bit of which I haven't really had a chance to digest yet. One thing, however, does jump out at me immediately as a problem:

His answer to my clarification on the next-to-last question would seem to fly in the face of any intuitive understanding of the notion of 'truth-preservation.'

For background, click through to the interview. The question provides a lot of detailed background on this. "ArT" means "A relates to Truth", which is a fancy way of saying "A is True." The idea here, as Priest has explained in other contexts, such as his article What is so bad about contradictions?, is that truth is conceived, not as a function, as classical logicians understand it, but as a relation, such that a proposition can be related to truth, to falsity or to both. In What is so bad about contradictions?, he includes a fourth option--A is related to neither truth nor falsity--but that option would seem to made superfluous by his arguments against the possibility of truth-value gaps in In Contradiction, and in any case the existence or non-existence of the fourth option isn't relevant to this discussion. DS is, of course, Disjunctive Syllogism, the classical inference from ~p and (pvq) to q. Since DS, plus the dialetheist's claim that p and ~p can sometimes both be true, quickly generates triviality, Priest and other dialetheists reject it. Priest's argument is, basically, that it isn't universally truth-preserving (and hence, isn't valid) because, given the assumption that some (but not all) contradictions are true, there can be cases in which ~p is true and (pvq) is true but in which q is not.

As he says in his response to me, "The DS can be show to be invalid is the semantics of LP as follows. (The semantics has many presentations. Let us use the version in which evaluations are relations, R, between formulas and the values t and f.

"Consider the inference ~p, pvq / q. Take an interpretation where pRt, pRf, qRf, and it is not the case that qRt. By the truth and falsity conditions for negation and disjunction, (~p)Rt and (pvq)Rt. Hence there is an evaluation where the premises of the inference relate to t and the conclusion does not. Hence the inference is invalid."

"Note that this argument...[is not] undercut if it turns out that there are formulas, A, such that ARt and it is not the case that ARt - even if you could show by some argument (goodness knows what), that this held when A is the p in question. Deductive reasoning is, after all, monotonic. (Valid arguments are never made invalid by the addition of extra premises.)"

So, why do I think all of this flies in the face of any intuitive notion of 'truth-preservation'?

Well, first of all, it seems to me that Professor Priest is being a bit coy when he speaks neutrally about the possibility of "ArT" and "it is not the case that ArT" being shown to be compatible--"if it turns out that there are formulas, A, such that ARt and it is not the case that ARt..." Given Priest's assumptions, *of course* there are such formulas! After all, we can always construct a sentence A such that A="It is not the case that ArT."

Secondly--and to the point--given that such formulas would seem to have to exist on Priest's account, when he's told us that there's an interpretation on which (~p)rT and (pvq)rT but it's not the case that qrT, he hasn't precluded the possibility that qrT--in other words, he hasn't precluded the possibility that, in this case, as in all other cases, true premises, fed into DS, generate a true conclusion!

Think of it this way--Priest would not claim that the mere existence of a case in which (~p)rT and (pvq)rT but in which qrF constituted a counter-example to DS, right? Given that it's as easy to generate a formula that both does and does not relate to truth as it is to generate one that relates to both truth and falsehood, why should truth-preservation be any more violated by the existence of a case in which q doesn't relate to truth than by a case in which it does relate to falsehood?